Metaheuristics are computational procedures that intelligently lead the search process through the efficient exploration of the search space associated with an optimization problem. With the progressive outburst of problems with large data sets in various fields, there is an ongoing quest for enhancing existing metaheuristic algorithms as well as developing new ones with greater accuracy and efficiency. In general, a powerful and efficient metaheuristic algorithm is based on a rich inspiration source, implemented effectively through a precise mathematical model. Aiming to develop a highly efficient, nature-inspired optimization algorithm, here we propose a novel metaheuristic called Crystal Structure Algorithm (CryStAl). This method is chiefly inspired by the principles underlying the formation of crystal structures from the addition of the basis to the lattice points, which is a natural phenomenon that can be seen in the symmetric arrangement of constituents (i.e. atoms, molecules, or ions) in crystalline minerals such as quartz. A total number of 239 mathematical functions which are categorized into four different groups are utilized to evaluate the overall performance of the proposed method. To validate the results of this novel algorithm, 12 different classical and modern metaheuristic algorithms are selected from the literature. The minimum, mean, and standard deviation values alongside the number of function evaluations for CryStAl and the other metaheuristics for a specific tolerance are calculated and presented accordingly. The obtained results, further supported by a complete statistical analysis, demonstrated that the proposed algorithm is capable of providing very competitive results, outperforming the other metaheuristics in most cases.

/pdf/crystal-structure-algorithm-crystal-a-metaheuristic-3v4tiir8o8.pdf

Crystal Structure Algorithm (CryStAl): A Metaheuristic Optimization Method

\n Flat-foldable origami tessellations are periodic geometric designs that can be transformed from an initial configuration into a flat-folded state. There is growing interest in such tessellations, as they have inspired many innovations in various fields of science and engineering, including deployable structures, biomedical devices, robotics, and mechanical metamaterials. Although a range of origami design methods have been developed to generate such fold patterns, some non-trivial periodic variations involve geometric design challenges, the analytical solutions to which are too difficult. To enhance the design methods of such cases, this study first adopts a geometric-graph-theoretic representation of origami tessellations, where the flat-foldability constraints for the boundary vertices are considered. Subsequently, an optimization framework is proposed for developing flat-foldable origami patterns with four-fold (i.e., degree-4) vertices, where the boundaries of the unit fragment are given in advance. A metaheuristic using particle swarm optimization (PSO) is adopted for finding optimal solutions. Several origami patterns are studied to verify the feasibility and effectiveness of the proposed design method. It will be shown that in comparison with the analytical approach and genetic algorithms (GAs), the presented method can find both trivial and non-trivial flat-foldable solutions with considerably less effort and computational cost. Non-trivial flat-foldable patterns show different and interesting folding behaviors and enrich origami design.

Particle Swarm Optimization-Based Metaheuristic Design Generation of Non-Trivial Flat-Foldable Origami Tessellations With Degree-4 Vertices

A prestressed cable-strut structure is usually regarded as a mechanism before being prestressed. Under the action of initial prestresses, the internal infinitesimal mechanisms can be rigidi...

Feasible Prestress Modes for Cable-Strut Structures with Multiple Self-Stress States Using Particle Swarm Optimization

Origami structures have attracted attention in biomedical applications due to their ability to develop surgical tools that can be expanded from a minimal volume to a larger and functional device. On the other hand, four-dimensional (4D) printing is an emerging technology, which involves 3D printing of smart materials that can respond to external stimuli such as heat. This short communication introduces the proof of concept of merging origami and 4D printing technologies to develop minimally invasive delivery of functional biomedical scaffolds with high shape recovery. The shape-memory effect (SME) of the PLA filament and the origami designs were also assessed in terms of deformability and recovery rate. The results showed that herringbone tessellation origami structure combined with internal natural cancellous bone core satisfies the design requirement of foldable scaffolds. The substantial and consistent SME of the 4D printed herringbone tessellation origami, which exhibited 96% recovery compared to 61% for PLA filament, was the most significant discovery of this paper. The experiments demonstrated how the use of 4D printing in situ with origami structures could achieve reliable and repeatable results, therefore conclusively proving how 4D printing of origami structures can be applied to biomedical scaffolds.

4D Printing of Origami Structures for Minimally Invasive Surgeries Using Functional Scaffold

Post-local buckling failure of slender and over-design circular CFT columns with high-strength materials

National Natural Science Foundation of China (Grant No. 51850410513 and No. 
51508089), and the Fundamental Research Funds for the Central Universities; Alexander von Humboldt-Foundation.

/pdf/an-integrated-geometric-graph-theoretic-approach-to-8qgm8tf9v6.pdf

An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks

Nodal flexibility and kinematic indeterminacy analyses of symmetric tensegrity structures using orbits of nodes

For pin-jointed assemblies with many members or self-stress states, the form-finding problem using conventional methods generally involves considerable computational complexities due to the large size of the solution spaces. Here, we propose an improved form-finding method for prestressable pin-jointed structures by combining symmetry-based qualitative analysis with particle swarm optimization. Expressed in the symmetry-adapted coordinate system, the nodal coordinate vectors of a structure with specific symmetry and topology are independently extracted from the key blocks of the small-sized force density matrices associated with rigid-body translations. Then, the first block of the equilibrium matrix is computed, in which the null space reveals integral self-stress states. Particle swarm optimization is introduced and adapted to find feasible prestress modes, where the uniformity and unilaterality conditions of the members are considered. Besides, the QR decomposition with column pivoting is adopted for efficient computations on the null space of these blocks. The QR decompositions of the small-sized blocks of the force density matrix and the equilibrium matrix are performed iteratively, to simultaneously find a stable self-equilibrium configuration and a feasible prestress mode. Representative examples show the presented method is computationally efficient and accurate for the form-finding of symmetric tensegrities and prestressed cable–strut structures.

Jiayi Yan

Papers

Particle Swarm Optimization-Based Metaheuristic Design Generation of Non-Trivial Flat-Foldable Origami Tessellations With Degree-4 Vertices

Feasible Prestress Modes for Cable-Strut Structures with Multiple Self-Stress States Using Particle Swarm Optimization

An Integrated Geometric-Graph-Theoretic Approach to Representing Origami Structures and Their Corresponding Truss Frameworks

Nodal flexibility and kinematic indeterminacy analyses of symmetric tensegrity structures using orbits of nodes

A hybrid symmetry–PSO approach to finding the self-equilibrium configurations of prestressable pin-jointed assemblies